Question 213396
A gardener has 46 ft of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.  If the length of the garden is twice its width what will be the dimensions of the garden?


Step 1.  Let L=2w be the length of garden and let w garden


Step 2.  Let L+2 and w+2 include the border

Step 3.  Let P = 46  ft be the perimeter.  Perimeter means adding the 4 sides of a rectangle.  So,


{{{P=L+2+L+2+w+2+w+2=2L+2w+8=2(2w)+2w+8=6w+8}}}


{{{P=46=6w+8}}}


Step 3.  Subtract 8 from both sides of equation

 
{{{46-8=6w+8-8}}}


{{{38=6w}}}


Step 4.  Divide 6 to both sides of equation to get w by itself



{{{38/6=6w/6}}}


{{{w=19/3}}}


Step 5.  w = 19/3 is the width of the rectangle and length L is 38/3  since {{{L=2w)}}}.   With the border w+2=25/3 and 2w+2=44/3  


Check P=6w+8= 6*(19/3)+8= 46 So w = 25/3 ft and L=44/3 is the solution.


Hope the above steps were helpful.  Good luck in your homework and studies!  


Respectfully
Dr J


Hope you understood and followed the steps. Good luck in your studies. Dr J 


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